1. Importance of Cardiac Output
A physician's ability to determine a patient's cardiac output ({dot over (Q)}, the volume of blood pumped by the heart each minute) is important in the assessment of critically ill patients. There are various devices and methods that provide a direct or indirect measure of {dot over (Q)} (see table 1). The most common method used in clinical practice is thermo-dilution, established by Ganz et al (1). Commercially manufactured catheters (referred to as Swan-Ganz catheters, named after the inventors) contain multiple lumina, an embedded thermister, and a balloon at the tip. The method requires the insertion of the catheter through the skin to access a large central vein such as the internal jugular, subclavian, cephalic or femoral. When the balloon at the end of the catheter is inflated, the catheter tip is carried along with the flow of blood to the right ventricle of the heart and then into the pulmonary artery. The part of the catheter that remains outside the body has connections that can be attached to electrical sensors that determine the pressure and temperature in the pulmonary artery where the tip of the catheter is positioned. Calculation of {dot over (Q)} requires the injection of a fixed volume of cool liquid of known temperature into a lumen of the catheter that has its opening part way along its length (usually in a part of the catheter in the right atrium). The thermister at the tip of the catheter will register changes in temperature as the cool liquid, carried by the blood, passes. The extent of dilution of the cold bolus of liquid by warm blood will determine the temporal profile of the temperature change at the tip of the catheter. This is referred to as the thermodilution method of measuring cardiac output(TD{dot over (Q)}).
The popularity of TD{dot over (Q)} stems from ease of use once the catheter is in place. However, the placing and maintenance of the catheter entails considerable risk and expense. Insertion of the Swan-Ganz catheter is associated with complications that are frequently fatal such as puncture of the carotid or subdavian artery with associated internal haemorrhage or stroke, tension pneumothorax, rupture of the right ventricle, malignant arrhythmias (including fatal ventricular fibrillation), and rupture of the pulmonary artery. As a foreign body violating the skin barrier, a pulmonary artery catheter is a constant threat as a source of blood-born infection that is the greatest risk to heart valves, artificial joints, and other implants. Such infections are medical disasters leading to severe morbidity and death. Furthermore, the use of pulmonary artery catheters to measure TD{dot over (Q)} is very expensive as it requires admission to an intensive care facility where there is continuous presence of critical care nursing and medical staff. Despite these risks, it is still not the ideal method to measure {dot over (Q)} as it tends to overestimate {dot over (Q)} by as much as 10% compared to the Fick method (see below) and, for greatest accuracy, requires repeated measurements as its precision is poor. The variability of repeated single measurements is about 22% and can be reduced to 10% by repeated averages of 3 measurements (2). A single thermodilution measurement is considered to be plus or minus 33% the true value. (3)
Because of the expense and risks of keeping the catheters in place, they are removed as soon as practical, often within 24-48 hours of major heart surgery. Often they are removed while the information they provide can still be clinically useful and well before the patient is no longer at significant risk for relapse. If the patient's health deteriorates, a decision must be made about re-inserting the catheter.
An automated non-invasive method of {dot over (Q)} monitoring would be very useful in the following clinical scenarios:                a) Selected low risk patients now routinely undergoing pulmonary artery catheterization for intra- and postoperative monitoring.        b) Patients whose {dot over (Q)} would be clinically important to know but in whom the risks and costs of insertion of a pulmonary catheter cannot be justified; this includes ward patients, outpatients or patients in the emergency department or doctor's office.        c) Patients who are too sick to warrant the added risk of pulmonary artery catheter insertion        d) High and moderate cardiac risk patients undergoing minor and moderate non-cardiac surgical procedures        e) Severely ill patients with non-cardiac disease.        f) Relatively healthy patients undergoing major stressful surgery.        g) Situations in which {dot over (Q)} is clinically indicated but there is no access to the expertise and critical care facilities required for the use of the pulmonary artery catheters.        h) Means of monitoring response to cardiovascular therapy such as for hypertension and heart failure.        i) As a non-invasive diagnostic test of cardiopulmonary status.        j) As a means of assessing cardiovascular fitness.        
Despite these many applications, non-invasive methods of {dot over (Q)} measurements have not obtained widespread clinical acceptance. The most commonly researched methods include ECG bio-impedance (Imhoff, 2000 (4)), and pulsed-wave Doppler esophageal sonography. These methods have good repeatability (5-12) and good limits of agreement with either thermodilution or Fick-based methods but only in some populations of subjects. Each method fails in certain patients groups with such pathologies as very high or low {dot over (Q)} states as occur in surgical patients, septic shock, exercise or cardiogenic shock.
2. Background Physiology and Definition of Terms
Venous blood returns to the right side of the heart from the muscles and organs with reduced oxygen (O2) and increased carbon dioxide (CO2) levels. Blood from various parts of the body is mixed in the right side of the heart and pumped to the lungs via the pulmonary artery. The blood in the pulmonary artery is known as the mixed venous blood. In the lungs the blood vessels break up into a network of small vessels that surround tiny lung sacs known as alveoli. This network of vessels surrounding the alveoli provides a large surface area for the exchange of gases by diffusion along their partial pressure gradients. After a breath of air is inhaled into the lungs, it dilutes the CO2 left in the alveoli at the end of the previous expiration, thereby establishing a pressure gradient between the partial pressure of CO2 (PCO2) in the mixed venous blood (P vCO2) arriving at the alveoli and the alveolar PCO2 (PACO2). The CO2 diffuses into the alveoli from the mixed venous blood diminishing the PCO2 in the blood, and increasing the PCO2 in the alveoli until equilibrium is established between the PCO2 in alveolar capillary blood and the PCO2 in the alveoli. The blood then returns to the left side of the heart via the pulmonary vein and is pumped into the arterial system by the left ventricle. The PCO2 in the arterial blood (PaCO2) is now the same as that in the alveoli. When the subject exhales, the gas at the very end of exhalation is considered to have come from the alveoli and thus simultaneously reflects the PCO2 in the pulmonary capillaries and the alveoli; the PCO2 in this gas is called the end-tidal PCO2 (PETCO2).
The volume of gas breathed per minute, or minute ventilation ({dot over (V)}E), is measured at the airway opening (nose and/mouth) and is expressed in L/min. The volume of breathed gas distributed to the alveoli (and thus contributing to gas exchange) is termed the alveolar ventilation ({dot over (V)}A) and is also expressed in L/min. The part of {dot over (V)}E that does not contribute to gas exchange is termed dead space ventilation. This is divided into the anatomical dead space that consists of the trachea and other gas-conducting tubes leading from the nose and mouth to the alveoli, and the alveolar dead space that is collectively the alveoli that are ventilated but not perfused with blood.
The {dot over (V)}E during normal breathing provides the {dot over (V)}A that is required to eliminate the CO2 brought to the lungs. {dot over (V)}E is controlled by a feedback system to keep PaCO2 at a set level of approximately 40 mmHg. Under steady state conditions, the rate at which CO2 is exhaled from the lungs ({dot over (V)}CO2) is equal to the rate that it is brought to the lungs, which in turn is equal to the metabolic CO2 production. We define steady state as the condition in which the flux of CO2 at the lungs is equal to the CO2 production and the {dot over (V)}CO2, P vCO2 and PaCO2 remain steady. If the {dot over (V)}CO2 is diminished, the CO2 extraction from the mixed venous blood passing by the alveoli will be reduced resulting in an increase in the PaCO2 when that blood reaches the arterial system. As the blood traverses the body, it will pick up additional CO2 and will return to the pulmonary artery with a higher PCO2 than on its previous passage. The time between the change in {dot over (V)}CO2 and re reappearance of the blood with raised PCO2 in the mixed venous circulation is termed the recirculation time which is generally taken as 20-30 s in resting subjects.
3. The Fick Equation
The approach for respiratory-based methods for measuring {dot over (Q)} non-invasively is described by the Fick equation, a mass balance of any substance across the lungs. The Fick method was originally described for O2 as a method for determining pulmonary blood flow. The Fick relation states that the O2 uptake by the lung is equal to the difference between the pulmonary artery and systemic arterial O2 contents times the {dot over (Q)}. The blood contents originally had to be obtained invasively from blood samples. The same relation holds with respect to CO2. The advantage of using CO2 as the tracer is that mixed venous and arterial blood contents of CO2 may be determined non-invasively. The Fick mass balance equation for CO2 is:
      Q    .    =                    V        .            ⁢                          ⁢              CO        2                    (                        C          ⁢                      v            _                    ⁢                      CO            2                          -                              Ca            ⁢            CO                    2                    )      where {dot over (Q)} is the cardiac output, {dot over (V)}CO2 is the rate of elimination of CO2 at the lungs, C vCO2 and CaCO2 are the mixed venous and systemic arterial contents of CO2, respectively. {dot over (V)}CO2 can be measured by a timed collection of expired gas and measuring its volume and CO2 concentration. The term CaCO2 can be calculated using an estimate of arterial PCO2 (PaCO2) as derived from the PCO2 of end tidal gas (PETCO2). The hemoglobin concentration (easily obtained from a venous blood sample or a drop of blood from a finger prick) and the relation between blood PCO2 and CO2 content (available from standard physiology texts) are then used to calculate CaCO2.
However, C vCO2 is difficult to estimate. The PCO2 of mixed venous blood (P vCO2) is difficult to determine as true mixed venous blood is present only in the pulmonary artery, which is inaccessible from the surface. The air in the lungs is in intimate contact with mixed venous blood, but CO2 diffuses rapidly from the mixed venous blood into the alveoli before an equilibrium is established. The PCO2 of the expired gas therefore reflects this equilibrium PCO2 and not the PCO2 of mixed venous blood. The P vCO2 can be determined from expired gas only when there has been full equilibration with continuously replenished mixed venous blood or partial equilibration under controlled conditions that allow for back calculation of P vCO2 from the PCO2 in expired gas. Hence during rebreathing, the alveolar gas is not refreshed and the mixed venous blood continuously passes the alveoli such that an equilibrium is established whereby the PETCO2 reflects the PCO2 in mixed venous blood.
However, even in this scenario, the PCO2 is not that which exists in the pulmonary artery. Blood in the pulmonary artery has a relatively low PO2. Because of the Haldane effect, the low PO2 allows the CO2 to be carried by the hemoglobin at a relatively low PCO2. When the mixed venous blood is exposed to gas in the alveoli, O2 diffuses into the blood, binds to the hemoglobin and increases the PCO2 needed for a given CO2 content on the hemoglobin (the complimentary aspect of the Haldane effect). All methods based on full or partial equilibration of alveolar gas with P vCO2 take into account that the equilibration is to a virtual PCO2 that would exist if the CO2 content of the hemoglobin were the same as in mixed venous blood but the hemoglobin were saturated with O2. We refer to this as the oxygenated mixed venous PCO2 (P vCO-oxy). Because the relationship between PCO2 and content of CO2 in blood is known, C vCO2 can be calculated from both the true P vCO2 (as obtained, for example, from a pulmonary arterial blood sample) and P vCO2-oxy (as obtained by some of the non-invasive methods described below)1. 1 The Pv  CO2-oxy does not really exist but is a virtual number created by instantaneously oxygenating mixed venous blood before and diffusion of CO2 into the alveoli. The C vCO2 is the same in each.
4. Rebreathing—Equilibration Method
One method of measuring P vCO2-oxy was introduced by Collier in 1956, and is known as the equilibration method. A bag is pre-filled with a high concentration of CO2 (˜10-13%) and the subject exhales and inhales rapidly to and from the bag and PCO2 is monitored continuously at the mouth. The object of the test is to find the combination of bag volume and bag concentration of CO2 such that once the gas in the bag mixes with that in the lungs (the concentration of CO2 in the residual gas in the lung at the end of a breath in a healthy person is ˜5.5%), the partial pressure of CO2 in the lung is equal to that in mixed venous blood. A flat segment of the PCO2 tracing segment indicates that inspired and expired PCO2 are equal. To identify the true P vCO2-oxy, the flat segment must occur within the first 3-4 breaths, before recirculation raises the P vCO2-oxy (see FIG. 8).
4.1.1 Advantages of the Equilibration Method:
The capnograph reading is of gas equilibrated with P vCO2-oxy and can be considered a directly measured value as opposed to a value obtained from calculation or extrapolation.
4.1.2 Limitations of the Equilibration Method:                4.1.2.1 The CO2 concentration in the bag depends on bag size, the patient's lung volume, and the P vCO2-oxy—the last being the unknown value. Therefore, the concentration of CO2 in the bag must be individualized to the patient and thus found by trial and error. The method is therefore difficult to automate fully.        4.1.2.2 In practice, since the characteristic of a suitable endpoint (the plateau of PCO2) is subjective, identification of a suitable plateau is difficult to automate.        4.1.2.3 The manoeuvre of rebreathing from a bag is difficult to perform in mechanically ventilated patients and is therefore not suitable for such patients.        4.1.2.4 Inhaling 10-13% CO2 is very uncomfortable and most people cannot tolerate it. It is particularly uncomfortable to someone who is short of breath or exercising.        4.1.2.5 The method requires an external source of CO2. This makes testing equipment bulky and awkward.        4.1.2.6 The method requires that the subject hyperventilate in order to mix thoroughly the gas in the bag and the lungs before recirculation of blood takes place. This requirement limits the test to those subjects who can perform this manoeuvre and who can provide this degree of cooperation. This excludes patients who have severe lung disease, those who are too young, too confused or too ill to cooperate.        4.1.2.7 The test loads a considerable volume of CO2 into the subject's lungs and at the same time prevents CO2 from leaving the blood for the duration of the test This has negative consequences for the subject:                    4.1.2.7.1 Following the test, the subject must hyperventilate to eliminate the applied CO2 load as well as the volume of metabolically-produced CO2 not eliminated during the test. This may pose a considerable burden for some subjects with lung disease or exercising subjects who are already expending considerable effort to cope with their existing metabolic CO2 load.            4.1.2.7.2 A period of hyperventilation following the test is required to eliminate the CO2. This may be difficult for some subjects to perform and, consequently, they may experience respiratory distress for some time until their PCO2 is decreased.            4.1.2.7.3 Repeated tests must be delayed until the extra CO2 is eliminated and the baseline state re-established.            4.1.2.7.4 The test itself may distress the subject and alter the {dot over (Q)}.5. Rebreathing—Exponential Method                        
In this technique, a small amount of CO2 is placed in a bag and the subject asked to rebreathe from the bag. The PETCO2s of successive breaths will rise exponentially towards P vCO2-oxy. A rising exponential curve is then fit to the PETCO2s of these breaths to predict an asymptotic value that is assumed to be the P vCO2-oxy (See FIG. 17).
5.1 Advantages of the Exponential Method                5.1.1 There is no requirement for respiratory manoeuvres by the patient.        5.1.2 A smaller CO2 load is placed on the subject in order to perform the test.        
5.2 Limitations of the Exponential Method                5.2.1 This is an indirect test in which the P vCO2-oxy is not measured directly but calculated from data generated by a test.        5.2.2 As the metabolic production of CO2 is small compared to the size of the lung and bag, the rise of PCO2 occurs over a prolonged period. This severely limits the number of useful data points for accurate extrapolation from an exponential curve, before recirculation.        5.2.3 The most important limitation of this and other methods that use partial equilibration during rebreathing to extrapolate to an asymptote using a single exponential is that the assumptions underlying the method are incorrect. In fact, the method produces two different mathematical profiles: the one describing the washout of CO2 from the lung into the bag is a decreasing exponential whereas the second describing the build-up of CO2 released from the blood into the lung-bag mixture is an increasing exponential (13). Only after the gases in the lung-bag system have become well mixed do the two exponentials resolve to a single exponential. By then, very few breaths (if any) that can provide suitable data for extrapolation from a single exponential can be taken before recirculation.        5.2.4 A continually rising level of CO2 makes this test unpleasant in conscious patients, especially in those exercising or very ill.        5.2.5 The manoeuvre of rebreathing from a bag is difficult to perform in mechanically ventilated patients and is therefore not suitable for such patients.        5.2.6 The method requires an external source of CO2. This makes testing equipment bulky and awkward.        5.2.7 The test loads a volume of CO2 into the subject's lungs and at the same time prevents CO2 from leaving the blood for the duration of the test Although the extent of the CO2 load on the subject is less than with the equilibration method, the negative consequences for the subject, outlined in the section on the equilibration method discussed above, must be considered.        5.2.8 Priming the rebreathing bag with some CO2 improves the predictive qualities of the asymptote since every data point lies closer to the asymptote, but the increased CO2 concentrations increase the discomfort and the limitations approach those outlined above for the equilibration method.6.0 Calculating {dot over (Q)} without First Calculating P vCO2-oxy        
Gedeon in 1980 described a method of calculating {dot over (Q)} in ventilated patients via a differential Fick method that circumvents the need to calculate P vCO2-oxy. The underlying assumptions of the method are that {dot over (Q)} and P vCO2 will remain unchanged during a step change in lung CO2 elimination and alveolar PCO2 (PACO2) lasting less than a recirculation time (about 30 seconds). Gedeon proposed reducing lung CO2 elimination by reducing either the tidal volume or respiratory frequency setting of the ventilator. As a modification of this method, Orr et al. proposed leaving the ventilator settings unchanged and reducing lung CO2 elimination by temporarily interposing a dead space between the ventilator and the patient's airway resulting in a transient period of rebreathing previously exhaled gas.
6.1 Theoretical Basis of Gedeon/Orr Method:
The method applies to a subject being ventilated under control conditions in which CO2 elimination and PETCO2 are measured. A test manoeuvre consisting of a transient alteration in the CO2 elimination for a time less than a recirculation time is effected and the resulting “equilibrium” PETCO2 is noted. It is assumed that the {dot over (Q)} and P vCO2-oxy during the test are unchanged from control conditions. The Fick equation for these two conditions can be written as
            Q      .        =                            V          .                ⁢                                  ⁢                  CO          2                                      C          ⁢                      v            _                    ⁢                      CO            2                          -                              Ca            ⁢            CO                    2                                Q      .        =                            V          .                ⁢                                  ⁢                  CO          2          ′                                      C          ⁢                      v            _                    ⁢                      CO            2                          -                              Ca            ⁢            CO                    2          ′                    where {dot over (V)}CO2′ is the CO2 flux at the lungs during the test and CaCO2′ is the corresponding ‘new’ arterial content of CO2. These two equations can be combined to yield the differential form of Fick's equation:
      Q    .    =            Δ      ⁢                          ⁢              V        .            ⁢                          ⁢              CO        2                    Δ      ⁢                          ⁢                        Ca          ⁢          CO                2            where Δ denotes a “difference in”. Since the PaCO2 and P vCO2-oxy lie on the same CO2 dissociation curve, partial pressures of CO2 can be substituted for CO2 content to yield the following relation:
      Q    .    =            Δ      ⁢                          ⁢              V        .            ⁢              CO        2                    S      *      Δ      ⁢                          ⁢                        Pa          ⁢          CO                2            where S is the slope of the CO2 dissociation curve. like the conventional non-invasive CO2-based Fick method, the differential Fick method relies on predicting PaCO2 through measurements of PETCO2. However, instead of requiring a calculation of P vCO2-oxy, the differential Fick equation assumes no change in P vCO2-oxy over the duration of the test, and uses the measured quantities {dot over (V)}CO2 and {dot over (V)}CO2′ and well as PaCO2 and PaCO2′ (from PETCO2) to calculate the remaining unknown value in the equation: {dot over (Q)}.
6.2Advantages of Gedeon/Orr Method    6.2.1 The main advantage is that P vCO2 does not need to be calculated.    6.2.2 If the deadspace method is used to alter the {dot over (V)}CO2, then no change in breathing pattern is required.    6.2.3 The method can, theoretically, be fully automated. (In its present commercial form, the size of the interposed deadspace must still be altered manually).
6.3 Limitations of Gedeon/Orr Method
There are a number of limitations in applying Orr's method to spontaneously ventilating subjects.    6.3.1 In spontaneously breathing subjects, there is considerable breath-to-breath variation in breath size and breathing frequency resulting in a variation in PETCO2. This poses problems with respect to:    6.3.1.1 Identification of PETCO2 and PETCO2′. Long periods of baseline measurements are needed in order to average the end tidal values and identify the PETCO2 to be used as the baseline PETCO2 in the differential Fick equation. The test phase cannot last for more than about 30 seconds (due to recirculation), typically 5 breaths. This leaves little time to determine an accurate average PETCO2′. During prolonged baseline periods of observation, the condition of the patient may change.    6.3.1.2 Calculation of {dot over (V)}CO2. The variations in PETCO2 are related to variations in CO2 elimination but the relationship is not consistently reflected by the PETCO2. For example, assuming a subject breathing at rest with an average resting breath size, an interposed smaller breath may result in a lower PETCO2 (due to a smaller contribution of alveolar gas to the end tidal sample) but the CO2 elimination from that breath will be diminished. Conversely, a larger breath may result in the same PETCO2 as the resting breath but a greater volume of CO2 is eliminated. The commercial automated Gedeon method (NICO2, Novametrics Medical Systems, Wallingford, Conn., U.S.A.) measures the CO2 eliminated breath-by-breath and therefore must continuously average the values to measure {dot over (V)}CO2. The NICO2 method of calculating {dot over (V)}CO2 by real-time integration of continuous measurements of flow (with a pneumotachymeter) and CO2 concentration (with a capnograph) is fraught with potential for errors: a small error in the integration of these two signals with different time delays and time constants results in a much larger error in the calculation of {dot over (V)}CO2. In addition, the greater the variability of the breath size and CO2 concentrations, the longer the measurement time required for an accurate estimate of {dot over (V)}CO2.    6.3.2 Calculation of {dot over (V)}CO2′. Stable transient changes in {dot over (V)}CO2 cannot be achieved in conscious spontaneously ventilating patients:    6.3.2.1 Interposing a deadspace and raising their PCO2 will stimulate spontaneously breathing conscious subjects to increase their {dot over (V)}E and {dot over (V)}CO2 until the PETCO2 is restored.    6.3.2.2 Any change in breath size or frequency during a period of breathing, (a normal occurrence in spontaneously breathing people) changes the {dot over (V)}CO2 during that period. During inspiration, the deadspace gas is inhaled first followed by fresh gas. A decrease in a breath size or frequency diminishes the volume of fresh gas inhaled (and thus the {dot over (V)}CO2for that breath). An increase in breath size or frequency will result in an increased volume of fresh gas delivered to the alveoli.    6.3.2.3 Each breath is an independent event and there is no inherent method to compensate in a subsequent breath for changes in {dot over (V)}CO2 in the preceding breath. For the method to be implemented, therefore, measures must be taken to ensure that breath size and frequency stay absolutely constant during the test. The NICO2 method has no such built-in aspects. The method can therefore be used only in patients who have precisely uniform breathing pattern such as those that are paralysed and mechanically ventilated.    6.3.3 Identification of PETCO2-PaCO2 gradient. The Gedeon and Orr methods assume, or require the establishment of, a constant gradient between the PETCO2 and the PaCO2. The variation in PETCO2 is due to variations of distribution of fresh gas to various parts of the lung and any one breath does not reflect the overall state of CO2 exchange. On the other hand, such variations are not reflected in the PaCO2 which does reflect the overall exchange of CO2 and remains relatively constant. Therefore, variations in PETCO2 also confound the quantification of the PETCO2-PaCO2 gradient under control conditions. Although Orr provides a number of equations to correct for these limitations, these equations are empirical and do not necessarily apply to a particular patient. For example, they are applied whether or not there is irregular breathing.     The PETCO2 -PaCO2 gradient during the test phase when rebreathing occurs is unknown. In the presence of large alveolar deadspace (as commonly occurs in many ill patients) the PETCO2-PaCO2 gradient will change during the rebreathing phase. Orr provides some equations to correct for this but since the volume of the alveolar deadspace is unknown, the applicability of the formula to any particular patient is unknown. This further diminishes the accuracy of calculating PaCO2′.     The manoeuvres required to determine each of the terms required to calculate {dot over (Q)} ({dot over (V)}CO2, {dot over (V)}CO2′, PETCO2, PETCO2′ and PaCO2′) by the Orr/Gedeon/NICO2 method is awkward to implement and prone to errors in measurement in the presence of any variation in breath amplitude or breathing frequency as occurs in spontaneously breathing humans or animals.    6.3.4 The parameter calculated by the differential Fick method as practiced by Gedeon/Orr/Respironics is pulmonary blood flow ({dot over (Q)}p). Pulmonary blood flow may be less than the total cardiac output ({dot over (Q)}t) when, for example, some of the {dot over (Q)} is shunted from the right side of the circulation (superior vena cava, right atrium, right ventricle, pulmonary artery) into the left side of the circulation without passing through the lungs. This is referred to as “shunt” ({dot over (Q)}s). About 5% of venous blood bypasses the lungs (termed shunted blood) in healthy adults. Much larger shunts occur in many medical conditions such as congenital heart disease, surgical repair of some congenital heart diseases, pneumonia, pulmonary edema, asthma, pulmonary atelectasis, adult respiratory distress syndrome, obesity, pregnancy, liver disease and others. The differential Fick method does not include shunted blood in the calculation of {dot over (Q)} and other empiric corrections must be made to account for it.7.0 Kim-Rahn Farhi Method
7.1 Theory:
A unique maneuver was proposed by Kim, Rahn and Farhi, (J. Appl. Physiol. 21:1388-44. 1966.) as a way to calculate the oxygenated mixed venous PCO2 (P vCO2-oxy) as well as the true P vCO2 and PaCO2. It is based on a paradigm of taking a breath of O2, holding the breath, and exhaling slowly over a period equal to the recirculation time. Over this time of exhalation, the CO2 from the mixed venous blood will diffuse into the alveoli and O2 will be absorbed. The low PO2 in the red blood cells in the mixed venous blood maximizes the volume of CO2 that can be carried by hemoglobin. Oxygen from the alveoli diffuses into the red blood cells, raising the PO2 and decreasing the affinity of hemoglobin for CO2 (Haldane effect). This releases CO2 from the binding sites on the hemoglobin, making it available for diffusion into the alveoli. With breath holding, CO2 will accumulate in the alveoli and the alveolar PCO2 (PACO2) will rise until it no longer provides a gradient for diffusion from the blood. (This PCO2 is known as the oxygenated mixed venous PCO2 (P vCO2-oxy).) However, O2 will continue to diffuse as long as the PAO2 is greater than P vO2. Relatively little CO2 need diffuse into the alveoli to reach P vCO2-oxy compared to the volume of O2 that is available for uptake before the PO2 in the pulmonary capillary blood is in equilibrium with the PAO2. In other words, the equilibration of CO2 in the alveoli with the mixed venous blood will occur well before that of O2.
Since both O2 and CO2 are contained in the same physical volume, the changes in concentrations of each gas over a short period will reflect the rates of flux of that gas over the same period. Therefore, over a short period, the ratio of PCO2 to PO2will reflect the respiratory quotient, RQ (defined as the rate of CO2 diffusion from the blood into the alveoli divided by the rate of O2 absorption into the blood from the alveoli). The RQ will initially be highest at the beginning of the breath when the rate of CO2 diffusion into the alveoli is maximal, and will approach 0 when the alveolar PCO2 equals P vCO2-oxy. In vitro studies have shown that PACO2 equals the true P vCO2 when the RQ=0.32 and equals PaCO2 when RQ is equal to the patient's steady state RQ (typically ˜0.8).
7.2 Test Method
The method suggested for performing this test would require a subject to take a maximum breath of 100% O2 and exhale very slowly and maximally. Over the course of this exhalation, expired gas is sampled and analyzed continuously for both PO2 and PCO2. PO2 is graphed vs. PCO2 and the RQ is calculated from the instantaneous slope of tangents to the curves at various PCO2 values as follows:
  RQ  =            slope      -              (                              FeO            2                    *          slope                )            -              FeCO        2                    1      -              (                              FeO            2                    *          slope                )            -              FeCO        2            
These RQ values are then plotted against their respective PCO2 data points resulting in a linear relation as illustrated in FIGS. 4 and 5 of T. S. Kin, H. Rahn, and L. E. Farhi cited above.
7.3 Advantages of the Method.                7.3.1 This is the only known non-invasive method by which true P vCO2 can be calculated.        7.3.2 The method provides an estimate of PaCO2 not based on assuming a gradient between PETCO2 and PaCO2.        7.3.3 Data generated by the method can be used to calculate the O2 saturation of mixed venous blood.        
7.4 Limitations of the Kim-Rahn-Farhi Breath-Hold Method.
The main limitation of this method is that it requires the subject to have a large lung capacity, hold his breath, and exhale over a prolonged duration. Patients with conditions such as pulmonary fibrosis, pneumonia, adult respiratory distress syndrome, chronic obstructive lung disease, asthma, obesity, trauma, abdominal and chest surgery, mental obtundation, confusion, pregnancy and many others have marked limitations in their ability to take a large breath Patients are required to cooperate with their duration of breath holding and rate of exhalation. Many patients who are ill, exercising subjects, children and others are unable to perform this satisfactorily. This method is very awkward to automate or perform on ventilated patients.
8.0 Fisher Method
8.1 Theory
In a steady state, if a subject breathes in a PCO2 equal to P vCO2-oxy, there will be no gradient for gas exchange and the difference in PCO2 between the inspired PCO2 (PICO2) and the expired PCO2 (PECO2) will be 0. The volume of CO2 diffusing into the alveoli will be maximal when the difference between PICO2 and PECO2 is greatest, i.e., when the PICO2 is 0. Since the change in alveolar PCO2 (PACO2) varies directly as the volume of CO2 diffusing into the alveoli and the volume diffusing into the alveoli varies directly as the gradient, then the difference between the PICO2 and PECO2 will vary inversely as PICO2. In other words, graphing the difference between the PECO2 and PICO2 (PECO2−PICO2) vs. FICO2 will result in a straight line. Since subjects normally breathe room air (PICO2 equals 0 or O2 the control PETCO2 provides the first point on the graph. When subjects inhale gas with any constant value of PCO2, the PETCO2 at the end of an equilibration period not exceeding the time for recirculation will provide a second data point which can be used to define the straight line which crosses the X axis where PICO2 equals P vCO2-oxy.
8.2 Test Method:
The subject breathes via a non-rebreathing valve. The inspiratory limb is provided with either fresh gas or test gas with any PCO2. To perform a test, the inspired gas is switched from control gas to test gas for about one recirculation time. The PICO2 of the test gas, the PETCO2 just before the test (when PICO2 was 0), and the PETCO2 of the last breath before recirculation are used to calculate the P vCO2-oxy.
8.3 Advantages of the Prior Disclosed Previous Fisher Method:                8.3.1 Any low inspired concentration of CO2 such as 1% is adequate to generate a data point; therefore the subject need not get a large CO2 load.        8.3.2 This Fisher method extrapolates to the P vCO2-oxy from a linear function and is therefore easier to calculate and more accurate than with the partial rebreathing test in which data points are fit to an exponential curve for extrapolation to an asymptote.        8.3.3 The PICO2 can be any value, so accurate mixtures of gases are not required.        8.3.4 Assuming arterial PCO2 values (PaCO2) can be obtained from arterial blood sample, for example, the method measures total {dot over (Q)}, not just pulmonary blood flow.        8.3.5 The subject need not carry out any respiratory manoeuvre such as breath holding or hyperventilation.        8.3.6 The method does not entail any rebreathing. Therefore, O2 levels remain stable throughout the test and supplemental O2 is not needed.        
8.4 limitations of the Fisher Method.                8.4.1 Uniform breath size cannot be guaranteed in spontaneously breathing subjects. A change of breath size or breathing frequency during the latter parts of the test phase will affect the PETCO2 and thus the calculation of P vCO2-oxy. Furthermore, as the subjects are inhaling gas that contains CO2, they may be stimulated to take larger or more frequent breaths.        8.4.2 The test requires an external source of CO2. This must be supplied via a tank of CO2 and a gas blender or via a tank of premixed gas. If more than one test gas is required, then arrangements to blend additional gases must be made or more than one additional gas tank is required. This is inconvenient, costly, and adds complexity to the test method and additional bulk and weight to the test apparatus.        8.4.3 It is very complex to configure an automated system that works for both spontaneously breathing and mechanically ventilated patients.        8.4.4 There is no simple method to adapt currently available ventilators, anaesthetic machines or breathing circuits to provide a known and constant PICO2 for a fixed number of breaths.        8.4.5 The technique is difficult to adapt to anaesthetized patients breathing via a circle circuit in which both the test gas and the anaesthetic gases enter the circuit, especially in the presence of a CO2 absorber removing CO2 from the circuit.        